The question was taken direct from the book so I can't help you with that.

As for finding the asymptotes,
I did indeed make a typo. You're answer is correct.

I think I understand how you got to the asymptotes. You used the equation of a sinusoid without the cos in it. Cos (pi/2)= 0. And the 2pi/1 =2pi. k is some integer, or x in my book.
Put it together and you have the asymptote for everything that starts on the top two quadrants.